# Trigonometry: Polar and Rectangular Coordinates

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Convert the equation to polar coordinates and simplify.

1. a. xy = 1

b. (x^2 + y62)^2 = 2xy

Express the equation in rectangular coordinates.

2. a. r = 3sin(t)

b. r = 4cos3(t)

r^2 = 4sin2(t)

r = 4/(2 + cos(t))

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##### Solution Summary

This solution converts the first equation to polar coordinates and simplifies it, and expresses the second equation in rectangular coordinates.

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1. First x=rcos(t), y=rsin(t).

a. Xy=1.

(rcos(t))(rsin(t))=1

r^2(cos(t)sin(t)=1

r^2sin(2t)=2.

Therefore, the polar equation is r^2sin(2t)=2.

b. Since x^2+y^2=r^2

(r^2)^2=2r^2cos(t)sin(t),

We first cancel out r^2: r^2=sin(2t).

Therefore, the polar equation is ...

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